Paper: arXiv 2302.08819

Authors: Alexander Lipton, Adil Reghai

Abstract

Local Stochastic Volatility (LSV) models have been used for pricing and hedging derivatives positions for over twenty years. An enormous body of literature covers analytical and numerical techniques for calibrating the model to market data. However, the literature misses a potent approach commonly used in physics and works with absolute (dimensional) variables rather than with relative (non-dimensional) ones. While model parameters defined in absolute terms are counter-intuitive for trading desks and tend to be heavily time-dependent, relative parameters are intuitive and stable, making it easy to steer the model adequately and consistently with its Profit and Loss (PnL) explanation power. We propose a specification that first explores historical data and uses physically well-defined relative quantities to design the model. We then develop an efficient hybrid method to price derivatives under this specification. We also show how our method can be used for robust scenario generation purposes - an important risk management task vital for buy-side firms.\footnote{The authors would like to thank Prof. Marcos Lopez de Prado and Dr. Vincent Davy Zoonekynd for valuable comments.}

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces an innovative physical/dimensional-analysis perspective to Local Stochastic Volatility (LSV) modeling, creating scale-invariant relative parameters. It combines sound mathematical formulations for hybrid derivatives pricing with practical applications in PnL attribution and scenario generation.

Research Flowchart

  flowchart TD
    A[Goal: Stable LSV Model Calibration & Risk Management] --> B[Data Input: Historical Market Data & Derivatives Prices]
    B --> C[Methodology: Convert Dimensional Variables to Non-Dimensional Quantities]
    C --> D[Model Design: Scale-Invariant LSV Parameterization]
    D --> E[Computation: Efficient Hybrid Derivatives Pricing Engine]
    E --> F[Outcome 1: Intuitive, Time-Stable Relative Parameters]
    E --> G[Outcome 2: Robust Scenario Generation & Improved PnL Explanation]